GATE Overflow Test Series | Spatial and Analytical Aptitude | Test 1 | Question: 11

Question

Which among the following integers is the largest one that divides the product of any seven consecutive integers?

• A. $5040$
• B. $40320$
• C. $510510$
• D. $201600$

Comments

In this question we have to determine the ”Largest integer that divides the product of any seven consecutive integers”  ?
Am i interpreting the question correctly?

@Deepak Poonia

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From the ones given in the options

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So as 40320 divides 2*3*4*5*6*7*8 , why this is not the asnwer

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@JAINchiNMay

See the discussion in the comments of the “best answer”.

Answer 1

$1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 = 7! = 5040,$ it divides the product of seven consecutive integers.

Now, if we take any $7$ consecutive integers, it'll have a multiple of numbers from $2-7$. That means any consecutive sequence of integers will be a multiple of $5040.$

So, the correct answer is $(A).$

Comments

40320/5040=8

And @Deepak Poonia sir if we are taking consecutive numbers from 2,3...8 then B can do while A can't divide it

what wrong I have said?  Can you please explain 

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If 40320 can divide something, then so does 5040, But the converse it Not true.

40320 doesn’t divide 5040 which is product of first seven positive consecutive integers.

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Okay sir got the point...

Thanks!